Trigonometry

Trigonometry is a word derived from three Greek words - Tri meaning Three, Gon meaning Sides and Metron meaning to measure. Trigonometry is the study of relationships between the sides and angles of a triangle.

Trigonometric Ratios

If one of the trigonometric ratios of an acute angle is known, the remaining trigonometric ratios of the angle can be easily determined.

Sin A = a/c

Cos A = b/c

Tan A = a/b = Sin A/Cos A

Cosec A = 1/Sin A

Sec A = 1/Cos A

Cot A = 1/Tan A

The value of sin A or cos A never exceeds 1, whereas the value of sec A or cosec A is always greater than or equal to 1.

T-Ratios of Important Angles

Complementary Angles

sin (90° – A) = cos A, cos (90° – A) = sin A

tan (90° – A) = cot A, cot (90° – A) = tan A

sec (90° – A) = cosec A, cosec (90° – A) = sec A

Standard Trigonometric Identities

Sin2A + Cos2A = 1

Sec2A - Tan2A = 1

Cosec2A = 1 + Cot2A

Application of Trigonometry

The height or length of an object or the distance between two distant objects can be determined with the help of trigonometric ratios.

The line of sight is the line drawn from the eye of an observer to the point in the object viewed by the observer.

The angle of elevation of an object viewed, is the angle formed by the line of sight with the horizontal when it is above the horizontal level, i.e., the case when you raise your head to look at the object.

The angle of depression of an object viewed, is the angle formed by the line of sight with the horizontal when it is below the horizontal level, i.e., the case when you lower your head to look at the object.